The fundamental form of a second-order homogeneous Lagrangian in two variables
Differential Geometry
2007-05-23 v1
Abstract
We construct, for a second-order homogeneous Lagrangian in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the 'fundamental Lepage equivalent' associated with first-order Lagrangians defined on jets of sections of a fibred manifold. We show that this form may be defined on a fourth-order frame bundle but is not, in general, projectable to a bundle of contact elements
Cite
@article{arxiv.math/0512384,
title = {The fundamental form of a second-order homogeneous Lagrangian in two variables},
author = {D. J. Saunders},
journal= {arXiv preprint arXiv:math/0512384},
year = {2007}
}
Comments
20 pages